The 200 observations used for the estimates in Table 1 are in fkdat1.txt.  The first variable is the log of the running time, and the second variable is age.  Only non dominated times are used.

The WMA data are in fkdat2.txt.  These are the raw data before they have been normalized. 

The LQmin, LQml, NPmin, and NPml estimates in Table 1 were obtained using the Frontline Analytic Sover Platform as implemented for Excel.  The corresponding Excel files for the four models are:

fklqmin.xlsx
fklqml.xlsx
fknpmin.xlsx
fknpml.xlsx

Each file contains six worksheets labeled 5K, 10K, HALFMA, MA, 5000M and 10000M, corresponding to the six races analyzed.  To run the embedded Solver models, the user must be in the worksheet labeled 5K. Opening the Solver and pressing on the green arrow (the "solve" button) will run the models.

The spreadsheets are all structured similarly; details are provided below for fknpmin.xlsx 

Opening fknpmin.xlsx to the worksheet labeled 5K, the user will see boldfaced columns headed Age, Log Time (which is the logarithm of the observed record time if data for that age exists; zero otherwise), NPmin (which contains the values of the NPmin-model-estimated log times on the biological frontier), errosq (which is the squared error between observed and modeled times, or zero if there is no observation), <data (which equals the model-estimated log time if data exist; zero otherwise), 1st, 2nd and 3rd derivatives which are computed as first-differences between successive modeled log times, modeled 1st derivatives, and modeled 2nd derivatives respectively for ages 40 and above); and the Age Factors as defined equation (5) of the paper. Scrolling to right, the user will see a graph displaing observed and modeled log times for the 5K race.  The user will also see in cell U6 the sum of squared errors between observed and modeled times for *all* six races (this cell sums the squared errors across the worksheets for all races).  The user will also see in cells X5:X9 the fixed effects for each race relative to the 5K race. Pressing the solve button will run the model.

Also contained in fknpmin.xlsx is a worksheet labeled Figs_2_3 that contains the data used to produce these figures in the paper. The data in that worksheet are self-explanatory, and in addition to the observed and modeled times, include imputed World Master Athletics times as computed from the normed WMA age factors, which appear in Columns L and M.

The paper in addition reports 10 year rates of decline. The 10 year rate of decline for any model (and also for the World Master Athletics data) is computed for age t as

10 year rate of decline at age (k) = 100 * ((Age Factor(k) / Age Factor (k-10)) - 1)   


